Spatial coordinate measurement systems play an important role in manufacturing and certification processes. There are many types of coordinate measurement systems including electronic theodolite networks, total station systems, video photogrammetry systems, laser tracking systems, laser scanning systems, and coordinate measuring machines. Each of these systems produces coordinate measurements containing some degree of uncertainty. Often, the results from several different types of measurement systems must be combined in order to provide useful measurement results. When these measurements are combined, the resulting coordinate data set contains uncertainties that are a function of the base data sets and complex interactions between the measurement sets. ISO standards, ANSI standards, and others, require that estimates of uncertainty accompany all measurement data. This research presents methods for quantifying the uncertainty fields associated with coupled spatial measurement systems. The significant new developments and refinements presented in this dissertation are summarized as follows: 1) A geometrical representation of coordinate uncertainty fields. 2) An experimental method for characterizing instrument component uncertainty. 3) Coordinate uncertainty field computation for individual measurements systems. 4) Measurement system combination methods based on the relative uncertainty of each measurement's individual components. 5) Combined uncertainty field computation resulting from to the interdependence of the measurements for coupled measurement systems. 6) Uncertainty statements for measurement analyses such as best-fit geometrical shapes and hidden-point measurement. 7) The implementation of these methods into commercial measurement software. 8) Case studies demonstrating the practical applications of this research. The specific focus of this research is portable measurement systems. It is with these systems that uncertainty field combination issues are most prevalent. The results of this research are, however, general and therefore applicable to any instrument capable of measuring spatial coordinates. / Ph. D.